{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Setting the Stage: What Are We Trying to Do?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.misc\n",
    "import matplotlib.pyplot as pt"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's load an image file and apply a simple image processing operation: *Blurring*. In mathematical terms, we will replace each pixel with a (weighted) average of its neighbors and itself."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3/dist-packages/PIL/Image.py:665: ResourceWarning: unclosed file <_io.BufferedReader name='cat.jpeg'>\n",
      "  self.load()\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f889862e1d0>"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wFZFBGYsGBEsNEph5MhgM1Gg0tLe3p08++UR7e3tmla6vr6tSqahUKkm6cqvO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UwEiFPcCa6LAUlUATSBFJqwGsx83NuD8oCuA5mcnNSdO3fU3d2td999V++//34mX8fHxzOKgXPB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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f889865cc50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "u = scipy.misc.imread(\"cat.jpeg\").astype(np.float32).sum(axis=2)/(3*256)\n",
    "\n",
    "pt.imshow(u, cmap=\"gray\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now make `blurred_u`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 61,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "#clear\n",
    "blurred_u = np.zeros_like(u)\n",
    "blurred_u[1:-1, 1:-1] = (\n",
    "    2*u[1:-1, 1:-1]\n",
    "    + u[2:, 1:-1]\n",
    "    + u[:-2, 1:-1]\n",
    "    + u[1:-1, 2:]\n",
    "    + u[1:-1, 2:]\n",
    "    )/6\n",
    "u = blurred_u"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.image.AxesImage at 0x7f889856a4e0>"
      ]
     },
     "execution_count": 62,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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CjNbax6vqC1V1UVWnwzB8c2vtjar6sap6X1V9vKq+axiGL/TScPS/TPeKgjmT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\ntrr3ejCWYFT1MoDr7emS+opuUK//yFB9rEwxBs97LoDMYSlep5vIHMX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99rOfrd/+7d+u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\niKSpYIhImgqGiKSpYIhI2jd2hsrW425TjgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f88985942b0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pt.imshow(blurred_u, cmap=\"gray\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Now, one individual blurring process may be *fast*. (in the sense that it feels instantaneous)\n",
    "* But it already takes a number of rounds (and therefore a short while) if we want the picture to be visibly blurry.\n",
    "* It would take even longer if the picture were bigger than just 200x200 (0.04 Megapixels). For reference, my phone takes pictures with 13 Megapixels.\n",
    "* It would take even longer if (say) we were a web service that needed to blur millions of images for customers."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As it turns out:\n",
    "   \n",
    "* What we did there was *not efficient* in lots of ways.\n",
    "* Time to peel back the layers, see what's going on under the hood, and understand how to make this process very fast.\n",
    "* While we're at it: Writing something fast that can *just* blur images might be nice. But it would be far easier to justify the effort to do that if what we wrote was *fast* and *general*, i.e. if it could apply lots of different image processing operations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**So here we go:** Let's see what would go into designing our own *image processing language*."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.1+"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
